Methodology

What we compute, how we compute it, and where every number comes from.

Last audited 2026-05-06 · Published 2026-01-15

Reynolds number

The flow-regime indicator. Below Re = 2,300 flow is laminar; above Re = 4,000 it is fully turbulent; the band in between is genuinely transitional and any free calculator that claims a precise friction factor there is bluffing.

Re = ρ · v · D / μ = v · D / ν

Source: standard fluid-mechanics text (e.g. Frank White, Fluid Mechanics, Ch. 6). Implementation in packages/shared/src/pipe.ts → reynolds().

Hazen-Williams equation

Empirical head-loss for water in commercial-grade pipes. Single closed-form expression; no iteration. Valid in the envelope Re = 10⁴–10⁷ at near-room-temperature water.

h_f = 10.67 · L · Q^1.852 / (C^1.852 · d^4.87) SI: Q in m³/s, d in m, L in m, h_f in m of water.

Source: Hazen & Williams (1905), Hydraulic Tables. C-factor library cites ASHRAE 2021 Handbook Ch. 22, AWWA M11 (steel), AWWA M9 (concrete), and Cameron Hydraulic Data. Implementation: packages/shared/src/pipe.ts → hazenWilliamsHeadM().

Darcy-Weisbach equation

Physically-derived head-loss equation. Works for any Newtonian fluid given (ρ, μ). Used by the flagship pressure-drop calculator and the Darcy-Weisbach calculator.

h_f = f · (L/D) · v² / (2g) g = 9.80665 m/s² (NIST standard gravity).

Source: Darcy (1857), Weisbach (1845). Implementation: packages/shared/src/pipe.ts → darcyWeisbachHeadM().

Friction-factor correlations

Three correlations are implemented; the dispatcher picks the right one for the regime.

Laminar (Re ≤ 2,300): f = 64 / Re (exact).
Transitional (2,300 < Re < 4,000): linear interpolation between laminar and turbulent endpoints. The regime is genuinely undefined.
Turbulent (Re ≥ 4,000): Colebrook–White, iterated to 1e-10 tolerance, seeded from Swamee-Jain.

Colebrook–White (1939): 1/√f = −2 · log₁₀(ε/(3.7D) + 2.51/(Re·√f)) Haaland (1983, explicit, ±2%): 1/√f = −1.8 · log₁₀((ε/(3.7D))^1.11 + 6.9/Re) Swamee-Jain (1976, explicit, ±1%): f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re^0.9)]²

Source: Colebrook (1939), Haaland (1983), Swamee & Jain (1976) — all in ASCE/ASME journals. Implementation: packages/shared/src/pipe.ts → frictionFactor*().

Minor (fitting) losses

K-factor method, summed over all fittings on a segment.

h_m = Σ K_i · v² / (2g)

Source: Crane Technical Paper 410 (1988), Cameron Hydraulic Data 19th ed., Idel'chik Handbook of Hydraulic Resistance. The L/D values are cross-checked against Crane. 17 fittings shipped today — the library is in packages/shared/src/fittings.ts.

Fluid properties — water

Water density and dynamic viscosity polynomials fit to NIST IAPWS-IF97 saturated-liquid data, valid 0–100 °C at 1 atm. Density is accurate to ±0.05%, viscosity to ±2%.

Density (kg/m³): ρ(T) = 999.84 + 16.95×10⁻³T − 7.987×10⁻³T² − 46.17×10⁻⁶T³ + ... (higher-order terms in the source — see fluids.ts → waterDensityKgM3) Dynamic viscosity (Pa·s), Vogel form: μ(T) = A · 10^{B/(T+273.15−C)} A = 2.414·10⁻⁵, B = 247.8, C = 140 (best-fit to IAPWS).

Source: NIST WebBook, ASHRAE Handbook 2021 Ch. 1.

Other fluids

The flagship and Darcy-Weisbach calculators expose six fluids:

Water (NIST IAPWS-IF97)
Seawater (≈3.5% salinity, ASHRAE 2021 Ch. 31)
Propylene glycol 30% / water (ASHRAE 2021 Ch. 31 secondary-coolant tables)
Propylene glycol 50% / water (ASHRAE 2021 Ch. 31)
Mineral oil ISO VG 32 (typical industrial-grade hydraulic oil; verify against vendor for safety-critical work)
Diesel #2 (ASTM D975-typical)

For other fluids, override the kinematic viscosity manually using the Darcy-Weisbach calculator. The fluid library is in packages/shared/src/fluids.ts.

Pump-sizing equations

Total Dynamic Head: TDH = h_static + h_friction + h_pressure Hydraulic power: P_hyd = ρ · g · Q · H Wire-to-water efficiency: η = η_p × η_m NPSH available (suction lift): NPSH_a = (P_atm − P_vap) / (ρg) − h_suct,lift − h_{suct,friction}

Source: Cameron Hydraulic Data; Hydraulic Institute pump standards (ANSI/HI 14.6).

Velocity safety bands

The thresholds used by the flagship and the velocity-check tool:

v < 0.6 m/s: sediment-prone — solids settle, biofilm grows
0.6 ≤ v ≤ 2.4 m/s: safe operating velocity
2.4 < v ≤ 3.0 m/s: high — noise and erosion likely
v > 3.0 m/s: water-hammer risk on rapid valve closure

Source: ASPE Plumbing Engineering Design Handbook v.4 Ch. 4.

Unit conversions

All conversion factors used by the calculators:

1 ft = 0.3048 m (exact)
1 in = 0.0254 m (exact)
1 GPM (US) = 6.30901964 × 10⁻⁵ m³/s
1 psi = 6,894.757 Pa
1 bar = 100,000 Pa
1 ft of water-head ≈ 0.4335 psi at 60 °F
g = 9.80665 m/s² (NIST standard gravity)

Implementation: packages/shared/src/units.ts.

Audit & changelog

Tables, formulas, and fluid properties are reviewed against the cited primary sources on the "Last audited" date. The first-pass audit covered Hazen-Williams C-factors, Darcy roughness ε, fitting K and L/D, water property polynomials, and unit conversion factors. Pull-request history available on request.

This is intended as a working engineer's tool. For safety-critical design (fire-protection, chemical-process, life-safety), cross-check against vendor-published Cv and the local authoritative standard (NFPA, ASME B31.x, etc.).

References

ASHRAE Handbook of Fundamentals (2021), Ch. 1, Ch. 22, Ch. 31. American Society of Heating, Refrigerating and Air-Conditioning Engineers.
AWWA M11 — Steel Pipe: A Guide for Design and Installation. American Water Works Association.
AWWA M9 — Concrete Pressure Pipe.
Cameron Hydraulic Data, 19th ed. (Flowserve).
Crane Technical Paper No. 410 (1988). Flow of Fluids Through Valves, Fittings, and Pipe.
Colebrook, C. F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. Journal of the Institution of Civil Engineers, 11.
Moody, L. F. (1944). Friction factors for pipe flow. Transactions of the ASME, 66.
Haaland, S. E. (1983). Simple and explicit formulas for the friction factor. Journal of Fluids Engineering.
Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. ASCE J. Hydraulic Division.
NIST IAPWS-IF97 (1997). Industrial Formulation for the Thermodynamic Properties of Water and Steam.
ASPE Plumbing Engineering Design Handbook, v.4, Ch. 4.
Hydraulic Institute Standards (ANSI/HI 14.6) — Rotodynamic Pumps for Hydraulic Performance Acceptance Tests.